Question

Integral $\int_0^1\ln^2(t)\psi^8(-t)dt=\frac{7}{8}\zeta(3)$

score 136 · Answer 1 · 2023-12-28 19:51:10

136

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Integral $\int_0^1\ln^2(t)\psi^8(-t)dt=\frac{7}{8}\zeta(3)$

Published on 28 Dec 2023 - 19:51

score 144 · Answer 2 · 2024-01-28 11:19:36

144

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How to compute $\sum_{n=0}^{\infty} \frac{(-1)^n}{\cosh((n+\frac{1}{2}) \pi)}$

Published on 28 Jan 2024 - 11:19

score 93 · Answer 3 · 2024-02-01 19:06:50

93

Views

Does the theory of theta functions ever go beyond just random caulculations and ugly formulas?

Published on 01 Feb 2024 - 19:06

score 138 · Answer 4 · 2024-02-20 14:23:24

138

Views

Close form expression for an integral with z derivative of jacobi theta function

Published on 20 Feb 2024 - 14:23

score 36 · Answer 5 · 2024-02-20 15:02:15

36

Views

How does Jacobi form lives projectively on the torus $\mathbb{C}/(\mathbb{Z}+\tau \mathbb{Z})$?

Published on 20 Feb 2024 - 15:02

score 45 · Answer 6 · 2024-02-26 06:47:18

45

Views

Understanding the proof of Theorem 10.1 in Montgomery & Vaughan's Multiplicative Number Theory

Published on 26 Feb 2024 - 6:47

score 187 · Answer 7 · 2024-03-04 08:14:52

187

Views

Mistake computing $\sum_{n=1}^{+\infty} \frac{n}{e^{2\pi n}-1} = \frac{1}{24}-\frac{1}{8\pi}$

Published on 04 Mar 2024 - 8:14

score 23 · Answer 8 · 2024-03-08 12:36:24

23

Views

What is the transformation formula of Theta series associated the quadratic form over totally real field?

Published on 08 Mar 2024 - 12:36

score 194 · Answer 9 · 2024-03-17 13:31:22

194

Views

How to prove the equality of power series below?

Published on 17 Mar 2024 - 13:31

score 96 · Answer 10 · 2024-03-26 23:04:11

96

Views

Residue theorem and theta function identities

Published on 26 Mar 2024 - 23:04

score 215 · Answer 11 · 2015-01-10 06:27:58

215

Views

Derivation of Transformation for basic theta function

Published on 10 Jan 2015 - 6:27

score 212 · Answer 12 · 2015-01-14 12:12:42

212

Views

Mumford's proof of theta function convergence

Published on 14 Jan 2015 - 12:12

score 41 · Answer 13 · 2015-03-03 06:19:12

41

Views

Does this function appear in theory of modular forms?

Published on 03 Mar 2015 - 6:19

score 128 · Answer 14 · 2015-03-21 01:57:53

128

Views

A special case of triple product identity

Published on 21 Mar 2015 - 1:57

score 75 · Answer 15 · 2015-03-30 07:23:50

75

Views

Is there a limiting case for this sequence of infinite product representations for the theta function?

Published on 30 Mar 2015 - 7:23

List Question

Integral $\int_0^1\ln^2(t)\psi^8(-t)dt=\frac{7}{8}\zeta(3)$

How to compute $\sum_{n=0}^{\infty} \frac{(-1)^n}{\cosh((n+\frac{1}{2}) \pi)}$

Does the theory of theta functions ever go beyond just random caulculations and ugly formulas?

Close form expression for an integral with z derivative of jacobi theta function

How does Jacobi form lives projectively on the torus $\mathbb{C}/(\mathbb{Z}+\tau \mathbb{Z})$?

Understanding the proof of Theorem 10.1 in Montgomery & Vaughan's Multiplicative Number Theory

Mistake computing $\sum_{n=1}^{+\infty} \frac{n}{e^{2\pi n}-1} = \frac{1}{24}-\frac{1}{8\pi}$

What is the transformation formula of Theta series associated the quadratic form over totally real field?

How to prove the equality of power series below?

Residue theorem and theta function identities

Derivation of Transformation for basic theta function

Mumford's proof of theta function convergence

Does this function appear in theory of modular forms?

A special case of triple product identity

Is there a limiting case for this sequence of infinite product representations for the theta function?

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